FINDING THE MIDPOINT BETWEEN TWO POINTS
GOAL 2
The midpoint of a line segment is the point on the segment that is equidistant
from its end-points. The midpoint between two points is the midpoint of the line
segment connecting them.
THE MIDPOINT FORMULA
x1 + x2 y1 + y2
, .
The midpoint between (x1, y1) and (x2, y2) is 2
2
EXAMPLE 4
Finding the Midpoint Between Two Points
Find the midpoint between (º2, 3) and (4, 2). Use a graph to check the result.
SOLUTION
º2 + 4 3 + 2
2 5
5
, = , = 1, 2
2
2 2
2
䉴 The midpoint is 1, 52.
✓CHECK
From the graph, you can see that the
5
point 1, appears halfway between (º2, 3)
2
y
5
RE
FE
Computers
EXAMPLE 5
(4, 2)
1
and (4, 2). You can also use the distance formula
to check that the distances from the midpoint to
each given point are equal.
L
AL I
1, 52 (2, 3)
3
1
1
3
5 x
Applying the Midpoint Formula
You are using computer software to design a video game. You want to place a
buried treasure chest halfway between the center of the base of a palm tree and
the corner of a large boulder. Find where you should place the treasure chest.
SOLUTION
Begin by assigning coordinates to the locations
of the two landmarks. The center of the base of
the palm tree is at (200, 75). The corner of the
boulder is at (25, 175). Then use the midpoint
formula to find the point that is halfway
between the two landmarks.
25 + 200 175 + 75
225 250
, = , 2
2
2
2
y
(25, 175)
200
(112.5, 125)
150
100
(200, 75)
50
0
0
50
100 150 200 x
= (112.5, 125)
䉴
You should place the treasure chest at (112.5, 125).
12.6 The Distance and Midpoint Formulas
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